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September 10, 2025Open Journal of Mathematical AnalysisOpen Access

Compactness and maximal regularity in variable-exponent bochner spaces with applications to nonlocal evolution equations

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Authors

MEMogoi N. EvansROR. K. Obogi

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Overview

This paper demonstrates compact embeddings and maximal regularity in variable-exponent spaces, highlighting applications to nonlocal evolution equations.

Key Points

  • Sharp compactness criteria are established under log-Holder continuity conditions for variable-exponent spaces.
  • Maximal regularity estimates for time-dependent fractional operators reveal new connections between exponent functions and operator orders.
  • Fractal dimension dynamics are systematically analyzed in variable-order fractional PDEs, impacting solution behavior.
  • Innovative functional-analytic tools lead to boundedness properties for nonlinear operators in stochastic variable-exponent spaces.

Cite This Study

Evans et al. (2025) studied this question.

synapsesocial.com/papers/68c194029b7b07f3a0618898https://doi.org/10.30538/psrp-oma2025.0167
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